I suppose you are speaking about the callback from ESI ?
If it’s the case:

if you are in the case of a webapp

You just have to listen to the callback URL in your side, get the code/token (depending on you are in implicit auth or not) and do what you need with it

if you are in a desktop / mobile app

For mobile app, you can use custom protocols and your app can listen to this (iirc we can do this?). For a desktop app, the “easier” (and best way to do this I think) is to start a websocket that’ll listen on “localhost:port” to get your callback url (which you’ll set in developers.eveonline.com to be the same).

After, it’s always the same: you get the code/token and you deal with it while notifying the user he’s authed.

Btw, the callback URL in anycase must match the one you set in your application CCP’s side.

I hope it helps, since your question really lacks informations (language, what you are trying to do, etc etc)

As for the desktop app - remember that if your local port cannot be opened, you will not be able to authenticate in any way. Period. Some time ago I proposed multiple callback urls, but no feedback yet. Or is there some @Steve_Ronuken ?

For desktop: If you have a site, you can redirect to that as a backup (I simply 64base encode the string and display it on the webpage and allow the user to copy and paste it into jEveAsset), if you can not start your local server. I have two identical apps registrated, one for localhost and one for my site. You can also register with multiple ports in the same way. It does require you keep track of what app ID/secret was used to create each refresh token with, but, that is a do-able.